UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS

[Pages:12]UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

*0414909462*

CAMBRIDGE INTERNATIONAL MATHEMATICS Paper 2 (Extended)

Candidates answer on the Question Paper

Additional Materials:

Geometrical Instruments

0607/02 May/June 2010

45 minutes

READ THESE INSTRUCTIONS FIRST

Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples, paper clips, highlighters, glue or correction fluid. You may use a pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES.

Answer all the questions. CALCULATORS MUST NOT BE USED IN THIS PAPER. All answers should be given in their simplest form. You must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 40.

For Examiner's Use

This document consists of 10 printed pages and 2 blank pages.

IB10 06_0607_02/2RP ? UCLES 2010

[Turn over

2

For the equation

Formula List

2

ax + bx + c = 0

_ b?

x =

2_

b

4ac

2a

Curved surface area, A, of cylinder of radius r, height h.

A = 2rh

Curved surface area, A, of cone of radius r, sloping edge l. Curved surface area, A, of sphere of radius r.

A = rl

2

A = 4r

Volume, V, of pyramid, base area A, height h. Volume, V, of cylinder of radius r, height h. Volume, V, of cone of radius r, height h. Volume, V, of sphere of radius r.

A

c

b

B

a

C

1 V= Ah

3

2

V = r h

1 2

V = r h 3

V =

4 3 r

3

a

b

c

=

=

sin A sin B sin C

2

2

2

a = b + c ? 2bc cos A

1

Area =

bc sin A

2

? UCLES 2010

0607/02/M/J/10

1

Write 36 000 in standard form.

3 Answer all the questions.

Answer

2

(a) Find the value of

(i)

0

3,

(ii)

1

36 2 .

8

x

(b) 2 ? 2 = 2

Find the value of x.

Answer(a)(i) Answer(a)(ii)

2

3

3

Factorise completely 3x y ? 12y .

Answer(b) x =

Answer

For Examiner's

Use

[1]

[1] [1]

[1]

[2]

? UCLES 2010

0607/02/M/J/10

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4

4

y 4

3

2

1

?180?

?90?

0

?1

?2

?3

?4

90?

180?

The diagram shows the graph of y = f(x), where f(x) = asin(bx). Find the values of a and b.

270?

360? x

For Examiner's

Use

Answer a = Answer b =

[1] [1]

? UCLES 2010

0607/02/M/J/10

5

2

5

(a) Factorise 2x + x ? 6.

(b) Solve the equation.

2

2x = 6 ? x

Answer(a)

For Examiner's

Use

[2]

6

(a) 3log2 + 2log3 = logk

Find the value of k.

(b)

log 25

Find the value of

.

log 5

Answer(b) x =

or x =

[2]

Answer(a) k = Answer(b)

[2] [1]

? UCLES 2010

0607/02/M/J/10

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6

5

-4

7

p = and q =

1

2

(a)

Write 2p -

1 q as a column vector.

2

(b) Find q leaving your answer in surd form.

For Examiner's

Use

Answer(a)

[2]

8

(a) Simplify

72 - 50 .

Answer(b)

Answer(a)

(b)

Write

1 2- 3

in its simplest form by rationalising the denominator.

[2] [2]

? UCLES 2010

Answer(b)

0607/02/M/J/10

[2]

7

9

y

8

6

4 B

2

?8 ?6 ?4 ?2 0 ?2

A

x

2

4

6

8

?4

?6

?8

(a) Describe fully the single transformation which maps shape A onto shape B.

(b) Draw the image of shape A after a stretch, with y-axis invariant and scale factor 2.

For Examiner's

Use

[3] [2]

? UCLES 2010

0607/02/M/J/10

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8

For

10

Examiner's

Use

NOT TO

SCALE

A

55?

O

B C

20?

D

E

The points A, B, C and D lie on a circle, centre O. AB is a diameter, angle BAD = 55? and angle BDC = 20?. ABE and DCE are straight lines.

Find

(a) angle ABD,

(b) angle BCD,

Answer(a)

(c) angle AED.

Answer(b)

Answer(c)

[1] [1] [1]

? UCLES 2010

0607/02/M/J/10

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